Stress distributions in randomly excited structures

Abstract

The work analyses the distribution of dynamic stress in flatplate and cylindricalshell structures, such as are found in the cooling gascircuits of nuclearreactors, when vibrating in response to broad frequencyband excitation. Thevibration predominantly takes the form of bending waves.

Twoanalytical models are considered, namely the normal modeand the travelling wavemodels. The normal mode model is chosen to examine thedistribution of stress inregions away from any boundaries of the structure thetravelling wave model isused to predict variations of stress in the vicinityof a boundary ordiscontinuity. In order to simplify the analysis of localstress, an idealisedmodel of a diffuse, travelling bending wave field isassumed. Acceleration andstrain correlation experiments are used toinvestigate the. conditions necessaryto establish a good approximation to sucha field. It is found that such anapproximation is valid whenever more than tenmodes are excited simultaneously.An additional requirement for a cylindricalshell is that the frequency ofresponse must be above the cylinder’s ringfrequency.

Thetravelling wave model is used to predict the ratios ofmean square stress andstrain to mean square velocity averaged over thestructure. This ratio isconfirmed by experiment. Also, the mean square stressat a weld and a change ofsection is predicted in terms of the space averagedmean square stress. Theseresults are confirmed by experiment. All theseresults are found to beapplicable even when fewer than ten modes are excited.

Thenormal mode model is used to predict the standarddeviation of mean squarestress and acceleration from their space averagedvalues when more than tenmodes are excited. Experimental results show goodagreement with theory, whenmore than twenty to thirty modes are excited, whenless than that number ofmodes are available, the measured standard deviationis lower than thatpredicted.

Inboth sections of the work, the effect of structuraldamping on the validity ofthe analyses is found to be small. The total numberof normal modes excited isby far the most important consideration.

Finally,it is suggested how the results might form thebasis of a relativelystraightforward design method, and possible futureextensions of this areconsidered.

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